Non-Gaussian Lineshapes and Dynamics of Time-Resolved Linear and Nonlinear (Correlation) Spectra

Abstract

Signatures of nonlinear and non-Gaussian dynamics in time-resolved linear and nonlinear (correlation) 2D spectra are analyzed in a model considering a linear plus quadratic dependence of the spectroscopic transition frequency on a Gaussian nuclear coordinate of the thermal bath (quadratic coupling). This new model is contrasted to the commonly assumed linear dependence of the transition frequency on the medium nuclear coordinates (linear coupling). The linear coupling model predicts equality between the Stokes shift and equilibrium correlation functions of the transition frequency and time-independent spectral width. Both predictions are often violated, and we are asking here the question of whether a nonlinear solvent response and/or non-Gaussian dynamics are required to explain these observations. We find that correlation functions of spectroscopic observables calculated in the quadratic coupling model depend on the chromophore's electronic state and the spectral width gains time dependence, all in violation of the predictions of the linear coupling models. Lineshape functions of 2D spectra are derived assuming Ornstein-Uhlenbeck dynamics of the bath nuclear modes. The model predicts asymmetry of 2D correlation plots and bending of the center line. The latter is often used to extract two-point correlation functions from 2D spectra. The dynamics of the transition frequency are non-Gaussian. However, the effect of non-Gaussian dynamics is limited to the third-order (skewness) time correlation function, without affecting the time correlation functions of higher order. The theory is tested against molecular dynamics simulations of a model polar-polarizable chromophore dissolved in a force field water.

Vibrational Spectroscopic Map, Vibrational Spectroscopy, and Intermolecular Interaction

“…The response function formulation presented above is still valid, but they need to be evaluated explicitly including the resulting non-Gaussian fluctuations. [111][112][113][114][115][116][117][118][119][120] In these cases, the numerical integration of the Schrödinger equation (NISE) 121 and the non-linear exciton propagation (NEP) algorithms 122 should be of use. 110…”

“…referred sometimes as the 'cumulative vibrational mapping For this, standard water forcefields such as SPC/E 390,419 and TIP4P 378,410 were used to run MD simulations and generate the ensemble of configurations and distributions of the electric field. Intramolecular coupling matrix elements were also parameterized according to the functional form, 378,411 ( ) (113) where the j and k indices refer to the coupled vibrational chromophores and a, b and c are adjustable parameters.…”

Polarizability of the active site of cytochrome c reduces the activation barrier for electron transfer

“…It is tested by the ability to produce the fourth-order time correlation function of the energy gap in terms of the Stokes shift dynamics ( Supplementary Fig. S8 ) 56 . Overall, we cannot clearly assign κ G > 1 found in our simulations to the non-Gaussian character of the energy gap fluctuations.…”

Excitation dynamics of two level quantum systems coupled to Morse vibrations

“…However, the quadratic coupling is only the second term in the series expansion in the electron-phonon coupling potential. The realistic potentials are neither harmonic nor the interaction functions are simple power functions [12][13][14], and that may lead to novel physics and spectroscopy.…”